Instantons in complex geometry: PDF files with the talks

14-18 March 2011,
Laboratory of Algebraic Geometry,
Higher School of Economics,

Home | Venue | Schedule | Program | Poster | PDF

Laura Costa (Univ. de Barselona)
Linear Monads on Instanton bundles on hyperquadrics (PDF)

Monads appear in a wide variety of context within Algebraic Geometry. We will focus our attention on linear monads as a tool for constructing indecomposable vector bundles on hyperquadrics and on the particular case of instanton bundles on them. This is a joint work with R.M. Miro-Roig.

Adrian Langer (University of Warsaw)
Moduli spaces of framed perverse instantons on P^3 (PDF)

I will talk about moduli spaces of framed perverse instantons on P^3. As an open subset they contain the moduli space of framed instantons studied by I. Frenkel and M. Jardim. I will explain the connection with the moduli space of pairs on the blow up of P^3 along a line. I will also study the map between the Gieseker and Donaldson-Uhlenbeck partial compactifications of the moduli space of instantons on P^3. Finally I will construct a few counterexamples to earlier conjectures and results concerning these moduli spaces.

Rosa M. Miro-Roig (Univ. de Barcelona) Monday, Tuesday or Wednesday

In my talk, I will address the problem of giving a cohomological characterization of vector bundles on algebraic varieties. This is a longstanding problem in Algebraic Geometry which has its roots in an old paper by Horrocks where he gave a cohomological characterization of line bundles on projective spaces P^n.

In my talk, I will give a cohomological characterization of the bundle of p-differential forms on multiprojective spaces P^{n_1}\times ... \times P^{n_s} and a cohomological characterization of Steiner bundles on algebraic varieties. As a main tool I will use a generalized version of Beilinson's spectral sequence.

This is joint work with Costa and Soares

Alexander Schmitt (Freie Univ. Berlin)
Quiver Bundles (PDF)

In this talk, I will first review the "classical" formalism of quiver representations, with a view on sheaves and instantons on projective manifolds. Then, I will give a survey on results on quiver bundles on projective manifolds and their moduli spaces. At the end, I will present joint work with Garcia-Prada and Heinloth on the motive of the moduli space of Higgs bundles of rank four and odd degree on a compact Riemann surface.

Home | Venue | Schedule | Program | Poster | PDF

Laboratory of Algebraic Geometry and its Applications